Moreover, in analogy with the standard characterization of
closed Hurewicz cofibrations in terms of NDR pairs, May and
Sigurdsson give a criterion (see Lemma 5.2.4 of [1]})
which detects when a closed inclusion \(i\colon A\rightarrow X\)  in
\({K}/B\)  is an \(\bar{f}\) -cofibration.
Such an inclusion \(i\colon A\rightarrow X\)  in \({K}/B\)  is an
\(\bar{f}\) -cofibration if and only if \((X,A)\)  is a
fiberwise NDR pair in the sense that there is a map
\(u\colon X\rightarrow I\)  for which \(A = u^{-1}(0)\)  and a homotopy \(h\colon X\times _B I\rightarrow X\) 
over \(B\)  such that \(h_0 = \mathit {id}\) , \(h_t|_A = \mathit {id}_A\) 
for all \(0\le t\le 1\)  and \(h_1(x)\in A\)  whenever \(u(x) < 1\)
